Toric Degenerations and Moduli I

Speaker:

Valery Alexeev (Georgia)

Date and Time:

Monday, August 15, 2016 - 11:00am to 11:50am

Location:

Fields Institute, Room 230

Abstract:

I will begin by explaining the fundamental construction of a convex toric degeneration which has been rediscovered by many people and which appears in different guises in many fields of mathematics. I will illustrate it by giving examples of toric degenerations as varieties, as pairs, as cycles, and as subschemes. I will also explain the extension of this construction to degenerations of abelian varieties, and of hyperplane arrangements. In the second talk, I will apply the fundamental construction to making various combinatorial moduli spaces: of stable toric pairs, toric Hilbert scheme, toric Chow varieties, stable semiabelic varieties, and stable hyperplane arrangements. Time permitting, I will go over applications of the theory of degenerations of abelian varieties to a problem of extending various Torelli maps to compactified moduli spaces: for Jacobians, Prym varieties, Prym-Tyurin varieties, and Intermediate jacobians.

Scheduled as part of

Who we are

The Fields Institute is a centre for mathematical research activity - a place where mathematicians from Canada and abroad, from academia, business, industry and financial institutions, can come together to carry out research and formulate problems of mutual interest. Our mission is to provide a supportive and stimulating environment for mathematics innovation and education. Learn more about us.

The Fields Institute promotes mathematical activity in Canada and helps to expand the application of mathematics in modern society.

Everyone is welcome to register and participate in events at the Fields Institute.